4x^2+14x+14x-151=0

Solution for 4x^2+14x+14x-151=0 equation:

Simplifying
4x2 + 14x + 14x + -151 = 0

Reorder the terms:
-151 + 14x + 14x + 4x2 = 0

Combine like terms: 14x + 14x = 28x
-151 + 28x + 4x2 = 0

Solving
-151 + 28x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-37.75 + 7x + x2 = 0

Move the constant term to the right:

Add '37.75' to each side of the equation.
-37.75 + 7x + 37.75 + x2 = 0 + 37.75

Reorder the terms:
-37.75 + 37.75 + 7x + x2 = 0 + 37.75

Combine like terms: -37.75 + 37.75 = 0.00
0.00 + 7x + x2 = 0 + 37.75
7x + x2 = 0 + 37.75

Combine like terms: 0 + 37.75 = 37.75
7x + x2 = 37.75

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 37.75 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 37.75 + 12.25

Combine like terms: 37.75 + 12.25 = 50
12.25 + 7x + x2 = 50

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(x + 3.5) equal to 7.071067812 and -7.071067812.

Subproblem 1
x + 3.5 = 7.071067812

Simplifying
x + 3.5 = 7.071067812

Reorder the terms:
3.5 + x = 7.071067812

Solving
3.5 + x = 7.071067812

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 7.071067812 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 7.071067812 + -3.5
x = 7.071067812 + -3.5

Combine like terms: 7.071067812 + -3.5 = 3.571067812
x = 3.571067812

Simplifying
x = 3.571067812

Subproblem 2
x + 3.5 = -7.071067812

Simplifying
x + 3.5 = -7.071067812

Reorder the terms:
3.5 + x = -7.071067812

Solving
3.5 + x = -7.071067812

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -7.071067812 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -7.071067812 + -3.5
x = -7.071067812 + -3.5

Combine like terms: -7.071067812 + -3.5 = -10.571067812
x = -10.571067812

Simplifying
x = -10.571067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.571067812, -10.571067812}